Heavy quark effective theory computation of the mass of the bottom quark

Parameters of heavy quark effective theory from N f = 2 lattice QCD

“…Employing the non-perturbative β-function of the SF coupling and estimates from our quenched calculation on the effect of propagating uncertainties in g 2 (cf. appendix D of [13]), we can assess an uncertainty of about 0.05 inḡ 2 to translate via L 1 into an uncertainty in the b-quark mass of at most 0.5%, which is negligible compared to the present direct uncertainty in the quark mass renormalization discussed below.…”

“…The ALPHA collaboration has proposed to use the framework of Heavy Quark Effective Theory (HQET) [10,11] with a non-perturbative determination of the couplings [12]. Its implementation at the first order in 1/m h has successfully been applied in the quenched approximation [13][14][15][16]. In this paper we will report on our effort to realize our HQET program for N f = 2 flavors of dynamical quarks, leaving the phenomenological results for forthcoming papers.…”

“…As a consequence, the static quantities depend on the choice of one angle, that we call θ 0 , and the quantities computed at the next-to-leading order of HQET depend on three angles: θ 0 , θ 1 , θ 2 . So far in this work we have considered only what we call the standard choice of θ angles [13,14], namely (θ 0 , θ 1 , θ 2 ) = (0.5, 0.5, 1). When we change the values of θ i we change the set of observables, and thereby the matching conditions.…”

HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation

“…We choose to regularise the theory on the lattice although our approach is in principle independent of the specific regularisation. Almost all formulae are established in [17]. They are repeated here for the benefit of the reader to keep the paper self-contained, but for details, such as the exact consequence of spin symmetry, the reader is referred to [17].…”

“…Section 3 explains the details, in particular how lattice spacing errors are removed in each step. The work of [17] is here extended by a determination of all parameters in the action as well as those for the weak current A 0 including the terms of order 1/m b .…”